Termination of mechanical vibratory systems



July 23, 1957 W. VAN ROBERTS HAL 2,800,633

TERMINATION OF MECHANICAL VIBRATORY SYSTEMS Filed June 25, 1953 K Q A Mandy/W044 WEI/flue) i I 2 INVENTORS 7 l/l wme MMB. fay/e75 ATTORNEY TERMINATION F MECHANICAL VIBRATORY SYSTEMS Walter van B. Roberts and Ralph W. George, Princeton, N. J., assignors to Radio Corporation of America, a corporation of Delaware Application June 25, 1953, Serial 'No. 364,105

17 Claims. (Cl. 333-71) This invention relates to the termination of mechanical vibratory systems, and more particularly, to the termination of band pass mechanical filters.

Mechanical filters usually consist of aplurality of mechanical resonators mechanically coupled together in a chain. If the end resonators are mechanical, they may include electromechnical transducers so that electrical energy may be applied to a mechanical resonator at one end to make it vibrate, and electrical energy may be derived from the mechanical vibrations of the mechanical resonator at the other end of the chain. The mechanical resonators at the ends may be of magnetostrictive material with drive and take-off coils disposed around the respective mechanical resonators.

The design of a mechanical filter includes the determination of a proper terminating impedance which must be provided to prevent reflections from having a disturbing effect on the proper operation of the filter. The filter design may call for terminating impedance at one end or at both ends of the filter. The terminating impedance seen by the mechanical filter, ideally, should be a pure resistance varying with frequency in a particular manner depending on the filter design. There is no known practical way to provide such a varying resistance, but it is possible, according to the prior art, to provide a terminating resistance which is substantially constant over the frequency pass band of a fil-ter and satisfactory filters can be designed to work into such a constant resistance. A constant terminating resistance may be provided by a mechanical transmission line of proper uniform characteristic impedance and of sufiiciently great length so that reflections from the end are attenuated and do not return to the filter. A less constant terminating impedance can be provided by electrical resistance in the electrical circuit coupled to the mechanical resonators at the ends for drive and take-off purposes. The electrical impedance reacts back into the filter to provide mechanical terminating impedance. Both a long mechanical terminating lineand a resistor in the electrical circuit may be used together to provide terminating impedance for the filter.

When a long mechanical line is relied upon solely to provide the desired terminating impedance, the driveand take-off circuits must be loosely coupled to the mechanical resonators at the ends to prevent the impedance in the circuits from introducing appreciable additional mechanical loss. As a result of the loose coupling there is a considerable energy loss, called insertion loss, between the electrical input and the electrical output of the filter. When electrical impedance in the drive and take-off circuits is relied on solely to provide the required terminating impedance, the circuits are closely coupled to the mechanical resonators at the ends, and there is very little insertion loss in the filter. However, when the electrical drive and take-off circuits are relied upon for terminating impedance and are part of the filter contributing to its band pass characteristic, that is when the electrical circutis are theend resonators of the filter, the construction and use of the filter is greatly complicated by the fact States Patent O 'ice that the circuits necessarily include inductance and capacitance as well as resistance which must beaccurately determined and fixed in value. The electrical circuits, and the co-efiicients of coupling between the electrical circuits and themechanical resonators at the ends, must be carefully adjusted. The adjustments are difficult to make initially and are difficult to maintain. Changes, such as those dueto temperature, cause the terminating impedance seen by the filter at the frequency of operation of the filter .to depart from the value required to properly terminate thefilter. From the point of view of stability of tuning, it is desirable to have the filter tuning unaffected by small changes in the electrical circuits.

It is an object of this invention to provide an improved termination for a mechanical vibratory system, the termination presenting a constant impedance to the system despite changes such as those due to temperature, etc.

It is another object to provide an improved termination for a mechanical band pass filter wherein the termination presents a constant impedance over a band of frequencies wider than the pass band of the filter.

It is a further object to provide an electromechanical filter having combined transducer and terminating means whereby the insertion loss of the filter is minimized.

It is a still further object to provide terminating means which is more compact and effective than those previously known.

In one aspect, the invention comprises a mechanical filter having a terminating line with a characteristic impedance such that if it were infinitely long it would properly terminate the filter. The line may be of any length but preferably is a quarter wave in length at the frequency of operation of the filter to facilitate tuning. The line mechanically couples an end resonator of the filter to a ferrite resonator which is, in turn, tightly coupled to an electrical circuit having a predetermined Q.

By a construction wherein certain relations are established between the fractional bandwidth of the filter, the dimensions of the ferrite, the coefiicient of coupling between the ferrite and the electrical circuit, and the Q of the electrical circuit, a termination for the filter is provided having a constant desired impedance over a band of frequencies considerably broader, than, and including, the frequency pass band of the filter. The electrical circuit also provides electrical driving or take-off means for the filter.

In another aspect, the invention comprises a mechanical filter having a terminating line extending from an end resonator of the filter to a first terminating mechanical resonator and a mechanical coupling from the first terminating resonator to a second terminating mechanical resonator. The construction is such that the filter is ter minated in the proper impedance over a wide band of frequencies including the frequencies passed by the filter.

These and other objects and aspects of the invention will appear from the following description taken together with the appended drawings wherein:

Fig. l is a functional block diagram illustrating the invention in a broad aspect;

Fig. 2 is a representation of a magnetostrictive filter terrninatedat one end by means following the teachings of this invention and including an electrical circuit; and

Fig. 3 is a representation of a symmetrical half of a V magnetostrictive filter terminated at both ends by mewound around mechanical resonator 2.

impedance Zr. couples the system to a terminatin mechanical resonator 2 having a mechanical impedance Z. The resonator 2 is resonant at substantially the center frequency of the passband of the system 10. The line 1 is constructed to havethe mechanical impedance Zr. by proper choice of material and cross sectional dimension. The length may be any value including 'zero, but a length of a quarter wave at the frequency of. operation of the filter facilitates adjustment. Terminating mechanical resonator 2 is coupled to a resonant device 3 by coupling means 4 providing a coefficient of coupling K. Resonant device 3. maybe a resonant electrical circuit having a predetermined electrical'Q or a mechanical resonator having a predetermined mechanical Q. The resonant 7 device 3 is also resonant at substantially the center frequency of the passband of the system 10. If device 3 is an electrical circuit, the coupling 4 is provided by a coil If device 3 is a mechanical resonator, the coupling 4 is in the form of a mechanical coupling neck. The elements 1, 2, 3 and 4 g in Fig. 1 are constructed in such a manner as to satisfy the following equations:

Referring now to Fig. 2 for a description of a specific embodiment of the invention, there is shown a mechanical vibratory system in the form of a magnetostrictive band pass filter 10'. The filter includes a driven magnetostrictive resonator 12 at one end, an intermediate mechanical resonator 13 and an end mechanical resonator 14. These resonators are a half wave in length and are mechanically coupled together by means of quarter wave coupling necks 15 and 16. The design of the filter is such that it requires a terminating impedance at only one end. The other end is connected by a quarter wave mounting stub 17, to a quarter wave mounting slug 18. Resonator 12 is driven by magnetostrictive action by an electrical circuit including a vacuum tube 19 having an output coil 20 wound around the resonator. The coil 20 is loosely coupled to the driver resonator 12 so that the impedance in the electrical circuit causes very little damping of the resonator.

The filter 10 requires a termination at one end presenting a mechanical impedance Zn. A line 21 having a mechanical impedance Zr. mechanically connects the end resonator 14 of the filter to a ferrite resonator 22. As an indication of a suitable material for resonator 22, a ferrite consisting of 74.69 grams of NiO and 158.68 grams of Fez03 heated to 1400 degrees C. for 1.5 hours and then slowly cooled has been found to be quite good in all respects. An electrical circuit 23 is closely coupled to ferrite resonator 22 by means of coil 25. The circuit 23 also includes a capacitor 26 and a resistor 27 adjusted to give the circuit a predetermined Q. The signal developed across capacitor 26 in circuit 23 isapplied to the input electrodes of amplifier vacuum tube 28. A disk 29 of a metal having high electrical conductivity is cemented to the end of ferrite resonator 22 to serve as a shield restricting magnetic flux leakage from the ferrite into neck 21 and thereby reduce the electrical insertion loss of the system.

In the construction of the termination for filter10', the line 21 is made to have the required mechanical impedance Z1. by the use of ratio formulas since th e absolute calculation of mechanical impedance is quite complicated. Two mechanical members carrying longitudinal vibrations have relative mechanical impedances'according to the formula:

where v is the velocity of propagation of longitudinal waves, a is the density of the material and-D' is the diam- The line 21 is thus designed to have the required mechanL cal impedance relative to the mechanical impedance of end resonator 14.

The ferrite resonator 22 is given a length such that it resonates at the frequency in the center of the pass band of the filter, and the electrical circuit 23 is also tuned to be resonant at the frequency in the center of the pass band. The coupling coefficient K between the ferrite resonator 22 and circuit 23 is made as high as possible by winding coil 25 very close to ferrite resonator 22 and by other design considerations. Resonator 22 is preferably, but not necessarily, made of ferrite because ferrite has a high magnetic permeability and magnetostrictive constant which permits of a very high coefficient of coupling K. Other materials such as nickel may be suitable when the fractional bandwidth B of the filter is less than 0.5 pericent, i. e., the difference between the upper and lower frequencies passed by the filter is 0.5 percent of the centerband frequency. After K is made as large as is practical, the Q of electrical circuit is adjusted, as by varying the value of resistor 27, until the Q is equal to l/K. This insures that critical coupling exists between ferrite resonator 22 and circuit 23 and that the impedance presented to filter 10 will be practically constant over the pass band of the filter. Then a check is made to determine whether the Q of the electrical circuit is less than l/B where B is the fractional bandwidth of the filter. The Q should preferably be not more than one-half 1/ B. If the Q is not less than l/B, measures are taken to increase the coefiicient of coupling K and to reduce the Q of the electrical circuit until the foregoing formulas are satisfied. Finally, the ferrite resonator 22 is given a diameter such that its mechanical impedance satisfies the formula:

Zr.=ZK Q which can be rewritten:

In the operation of the terminated filter of Fig. 2, the ferrite resonator 22 presents a substantially constant mechanical impedance to the line 21 and filter 10 over a band of frequencies at least two times the pass band of the filter. The ferrite resonator 22 presents the substantially constant impedance by reason of its being critically coupled to electrical circuit 23. The filter remains terminated in the required impedance despite very considerable changes in the termination means such :as may be caused by temperature changes and manufacturing tolerances. A high level electrical output is derived from circuit 23.

Solely by way of example, a terminated filter using the torsional mode of vibration, was constructed according to the form shown in Fig. 2 with the filter 10 made of Ni span C and designed to provide a frequency pass band having a width of 0.25 percent of the centerband frequency of kilocycles. Terminating line 21 was 0.075 inch in diameter and was made of Ni span C. Ni span C is a nickel-iron alloy including 42 percent nickel, 5.5 percent chromium, 2.5 percent titanium, 0.06 percent carbon, 0.4 percent manganese, 0.5 percent silicone and 0.4 percent aluminum. The ferrite resonator 22 was a half wave long at 105 kilocycles, or approximately 0.660 inch, and had a diameter of 0.221 inch. THC Q of electrical circuit 23 was 110. The coefiicient of coupling K between the ferrite resonator 22 and the electrical circuit 23 was 0.009, and since this is 3.6 times the fractional bandwidth B of the filter, the termination provided a substantially constant impedance to the filter over a band of frequencies including and considerably greater aso esa than the pass band of the filter. Therefore, considerable variation in the factors affecting thefrequencies at which the termination provides the proper impedance is possible and yet the filteris properly terminated over the frequencies in its pass band.

Fig. 3 shows one half ofga terminated magnetostrictive filter which is symmetrical abouta center line. The filter design is such as to require termination in a predetermined mechanical impedance at bothends. The symmetrical half of the filter includes a plurality of half wave mechanical resonators coupled in a chain by quarter wave mechanical,smaller-diameter coupling necks. The end resonator 34 of-thefilter is of magnetostrictive material and is coupled by means of a coil 36 to a take-ofi circuit 37. The other half of the terminated filter (not shown) includesan end resonator driven by an electrical circuit and terminating resonators similar to resonators 42, 43. The filter ofFig. 3 isterminated at both ends solely by mechanical means. in order that the drive and take-off circuits shall not present disturbing mechanical impedances to the filter, these circuits are loosely coupled to the end resonators.

The terminating line 41 is constructed to have the desired mechanical impedance Zr. after the manner de scribed in connection with line 21 of Fig. 2. Line 41 is coupled to a first terminating half wave mechanical resonator 42,, which isin turn coupled to a second half wave terminating mechanical resonator 43 through a quarter wave coupling neck 44. The lengths of the first terminating mechanical resonator 42, the second terminating mechanical resonator 43, and the coupling neck 44 are in terms of the midband frequency. of the filter 10". The terminating means is constructed to satisfy the previously given formulas:

where Zr. is the mechanicalimpedance of line 41, Z is the mechanical impedance of resonator 42, K is the coefiicient of coupling between resonators 42 and 43, Q is the Q of the second terminating resonator 43 and B is the fractional bandwidth of the filter.

The Q of the second terminating resonator 43 is determined by the material of which it is constructed. A material having a very low Q should be selected. Cast iron or lead has been found to provide a sufiiciently low Q for terminating filters having a narrow pass band. The Qs of .various materials are shown in a table on page 35 6 of the September 1949 issue of the RCA Review, Volume X, No. 3. Then the required coefficient of coupling between the terminating resonators 42 and 43 is determined from Formula 2 above. A check is made to insure that the coefiicient of coupling K is at'least two times the fractional bandwidth B of the filter to satisfy Formula 3. If K is not high enough, a material having a lower Q is required for the second terminating resonator 43. Finally, the mechanical impedance Z required for the first terminating resonator 42 is determined from Formula 1. Brass or aluminum has been found to be a suitable material to use for the first terminating resonator 42. Impedance ratio formulas, such as those given in connection with the descriptionof Fig. 2, are used to determine the physical diameters of terminating resonators 42 and 43 and of coupling neck 44.

In the operation of the terminated filter of Fig. 3, the coupled terminating resonators 42 and 43 provide the desired terminating impedance to the filter over a band of frequencies which includes and is broader than the band of frequencies passed by the filter. Therefore, the filter remains terminated in the proper impedance despite very considerable changes in the termination means such as may be caused by temperature changes and manufacturing tolerances.

The terminating scheme shown in all the figures of the ,6 drawing may be thought of as a terminating filter designed to have a frequencypass band which is at least two times as broad as the pass band of the filter which is terminated thereby. The resonantdevices 3,23 and 43 in Figs. 1,

2 and 3 respectively are constructed to have a low Q thereby to provide the desired terminating impedance over a band of frequencies at least two times as broad asthe pass band of the filter.

It Willbe understood by those skilled in the art that the coupling means in the form of terminating lines 1, 21 and 41 in Figs. 1, 2 and 3, respectively, may have an impedance differing'frorn the impedance 2:. required to terminate the filter, and may be in the nature of a mechanical impedance transformer. Then the impedance presented by the termination is 7 not Zr. but may be designated ZT. The formulas for the construction of the termination become ZT=ZK2Q, KQ-1 and K B. If the transformer neck'replacing the terminating line is a quarter wave in length, the transformer neck will have an impedance which is the geometric mean between the impedances ZL and Zr. The transformer neck transforms the impedance Zr of the termination to the impedance Zr. required to properly terminate the filter.

What is claimed is:

'1. A terminated mechanical bandpass filter comprising, a plurality of mechanical resonators mechanically coupled together in a chain to provide a filter having a fractional frequencypass band B and requiring a terminating impedance ZL, coupling means connected at one end thereof to an end resonator of said filter to translate an impedance ZI at the other end thereof to said impedance ZL at said one end thereof, a mechanical terminating resonator having an impedance Z connected to said other end of said coupling means, and a resonant device having a predetermined Q and coupled to said mechanical terminating resonator with a coupling coefiicient K, said mechanical terminating resonator and said resonant device each being resonant at substantially the center frequency of said passband, and said mechanical terminating resonator and said resonant device being constructed to satisfy the formulas ZT=ZK2Q, KQ-1 and K B.

2. A terminated mechanical filter as defined in claim 1 wherein K is at least two times B.

3. A terminated mechanical band pass filter comprising, a plurality of mechanical resonators mechanically coupled together in a chain to provide a filter having a fractional frequency pass band B and requiring a terminating impedance ZL, a mechanical line'having a characteristic impedance Zr. coupled to an end resonator of said filter, a mechanical terminating resonator having an impedance Z coupled to said line at a point on said iine other than the point at which said line is coupled to said filter, and a resonant device having a predetermined Q and coupled to said mechanical terminating resonator with a coupling coefficient K, said mechanical terminating resonator and said resonant device each being resonant at substantially the center frequency of said passband, and said mechanical terminating resonator and said resonant device being constructed to satisfy the formulas 4. A terminated mechanical filter as defined in claim 3 wherein K is at least two times B.

5. A terminated mechanical band pass filter comprising, a plurality of mechanical resonators mechanically coupled'together in a chain to provide a filter having a fractional frequency pass band B and requiring a terminating impedance Zn, a mechanical terminating line having a characteristic impedance Zr. coupled to an end resonator of said filter, a magnetostrictive resonator connected to said line at a point on said line other than the point at which said line is coupled to said filter, and an electrical circuit substantially critically coupled to said magnetostrictive resonator with a coefficient of coupling K, the product of the Q of the electrical circuit, K and the impedance of the magnetostrictive resonator being equal to ZL, and said magnetostrictive resonator and said electrical circuit each being resonant at substantially the center frequency of said passband.

6. A terminated mechanical filter as defined in claim wherein the coefficient of coupling K is at least two times the fractional bandwidth of the filter.

7. A terminated mechanical band pass filter comprising, a plurality of mechanical resonators mechanically coupled together in a chain to provide a filter having a fractional frequency pass band B and requiring a terminating impedance Zn, a mechanical terminating line having a characteristic impedance Zn coupled to an end resonator of said filter, a first terminating mechanical resonator coupled to said line at a point on said line other than the point at which said line is coupled to said filter, said first terminating mechanical resonator heaving an impedance Z and being resonant at substantially the center frequency of said passband, a second terminating mechanical resonator made of a material having a relatively low Q, said second terminating mechanical resonator being resonant at substantially the center frequency of said passband, a coupling neck coupling said terminating resonators together with a coefficient of coupling K which is larger than B, said values being such as to satisfy the formula ZL=ZK2Q.

8. A termination for a mechanical transmission line having a characteristic impedance Zr. comprising a pair of resonant devices substantially critically coupled together with a coefiicient of coupling K, both of said resonant devices being resonant at substantially the same frequency, the first of said devices having a mechanical impedance Z and the second of said devices having a predetermined Q, said values being such that ZK2Q=ZL, the first of said devices being mechanically connected to said transmission line.

9. A terminated mechanical band pass filter comprising, a plurality of mechanical resonators mechanically coupled together in a chain to provide a filter having a fractional frequency pass band B and requiring a terminating impedance Zn, a mechanical transformer connected at one end thereof to an end resonator of said filter to transform an impedance Z'r at the other end thereof to said impedance Zr. at said one end thereof, a mechanical terminating resonator having an impedance Z connected to said other end of said transformer and a resonant device having a predetermined Q and coupled to said mechanical terminating resonator with a coupling coelficient K, said mechanical terminating resonator and said resonant device each being resonant at substantially the center frequency of said passband, and said mechanical terminating resonator and said resonant device being constructed to satisfy the formulas ZT=ZK2Q, KQ-1 and K B.

10. A terminated mechanical filter as defined in-claim 9 wherein said resonant device is an electrical circuit.

11. A terminated mechanical filter as defined in claim 9 wherein said resonant device is a mechanical resonator.

12. A terminated mechanical filter as defined in claim 9 wherein K is at least two times B.

13. A termination for a mechanical transmission line having a characteristic impedance Zr. over a band. of frequencies comprising a pair of resonant devices substantially critically coupled together with a coefficient of coupling K, both of said resonant devices'being substantially resonant at the center frequency of said band of frequencies, the first of said devices having a mechanical impedance Z and the second of said devices having a predetermined Q, said coefficient of coupling K, said mechanical impedance Z, and said Q having values such that ZK Q=Zr., and means for coupling the first of said devices to said transmission line.

14. The combination with an electromechanical filter of additional means constituting a termination for said filter, said additional means comprising a mechanical transmission line having a characteristic impedance ZL, a pair of resonant devices substantially critically coupled together with a coefficient of coupling K, said pair of resonant devices both being resonant at substantially the midband frequency of said electromechanical filter, the first of said devices having a mechanical impedance Z and the second of said devices having a predetermined Q, said values being such that ZK Q=Z and means for coupling the first of said devices to said transmission line at a point other than the point at which the second of said devices is coupled to the first of said devices.

15. A terminated mechanical filter comprising a bandpass filter having a fractional bandwidth B and requiring a terminating impedance ZL, a termination for said filter comprising a magnetostrictive resonator having an impedance Z, said magnetostrictive resonator being resonant at substantially the center frequency of said bandpass filter, means coupling said magnetostrictive resonator to said mechanical filter, and an electrical circuit coupled to said magnetostrictive resonator with a coefiicient of coupling K greater than said fractional bandwidth B, said electrical circuit being resonant at substantially the center frequency of said bandpass filter, and said termination presenting an impedance ZK2Q=ZL to said filter, where Q is the Q of said electrical circuit.

16. A terminated mechanical filter comprising a bandpass filter having a fractional bandwidth B and requiring a terminating impedance ZL, a termination for said filter comprising a first mechanical resonator having an impedance Z coupled to said filter, and a second mechanical resonator having a predetermined Q, said resonators each being resonant at substantially the center frequency of said bandpass filter, said resonators being coupled together at a point other than the point said first mechanical resonator is coupled to said filter with a coefiicient of coupling K greater than said fractional bandwidth B, and said termination presenting an impedance ZK2Q=ZL to said bandpass filter.

17. A termination for a mechanical transmission line having a characteristic impedance Zr. over a band of frequencies B, comprising a pair of resonant devices substantially critically coupled together with a coefficient of coupling K, both of said resonant devices being substantially resonant at the center frequency of said band of frequencies B, the first of said devices having a mechanical impedance Z and the second of said devices having a predetermined Q, said coefiicient of coupling K, said impedance Z, and said Q having values such that ZK2Q=ZL and Qg /zB, and means for coupling the first of said devices to said transmission line.

References Cited in the file of this patent UNITED STATES PATENTS 2,495,740 Labin et al. Ian. 31, 1950 2,571,019 Donley et al. Oct. 9, 1951 2,578,452 Roberts Dec. 11, 1951 2,617,882 Roberts Nov. 11, 1952 2,619,604 Burns Nov. 25, 1952 2,647,948 Roberts et a1. Aug. 4, 1953 2,652,543 Anthony et al Sept. 15, 1953 2,762,985 George Sept. 11, 1956 OTHER REFERENCES Roberts et al.: RCA Review, September 1949, PP- 348- 365. 

